Particle Entity in the Doi-Peliti and Response Field Formalisms

TL;DR

This paper develops a method to verify if field theories correctly incorporate the discrete particle nature of systems, focusing on Doi-Peliti and Dean's equation frameworks, with implications for active matter research.

Contribution

It introduces a procedure to test particle entity in field theories and uncovers diagrammatic identities in Dean's equation, enhancing understanding of particle representation in these models.

Findings

Doi-Peliti theory explicitly encodes particle nature

Dean's equation involves complex diagrammatic identities

Results are relevant for active matter modeling

Abstract

We introduce a procedure to test a theory for point particle entity, that is, whether said theory takes into account the discrete nature of the constituents of the system. We then identify the mechanism whereby particle entity is enforced in the context of two field-theoretic frameworks designed to incorporate the particle nature of the degrees of freedom, namely the Doi-Peliti field theory and the response field theory that derives from Dean's equation. While the Doi-Peliti field theory encodes the particle nature at a very fundamental level that is easily revealed, demonstrating the same for Dean's equation is more involved and results in a number of surprising diagrammatic identities. We derive those and discuss their implications. These results are particularly pertinent in the context of active matter, whose surprising and often counterintuitive phenomenology rests wholly on the particle nature of the agents and their degrees of freedom as particles.